Download The Deaths of Very Massive Stars

The Deaths of Very Massive Stars
arXiv:1406.5657v1 [astro-ph.SR] 21 Jun 2014
S. E. Woosley and Alexander Heger
Abstract The theory underlying the evolution and death of stars heavier than 10 M⊙
on the main sequence is reviewed with an emphasis upon stars much heavier than
30 M⊙ . These are stars that, in the absence of substantial mass loss, are expected
to either produce black holes when they die, or, for helium cores heavier than about
35 M⊙ , encounter the pair instability. A wide variety of outcomes is possible depending upon the initial composition of the star, its rotation rate, and the physics
used to model its evolution. These heavier stars can produce some of the brightest
supernovae in the universe, but also some of the faintest. They can make gammaray bursts or collapse without a whimper. Their nucleosynthesis can range from
just CNO to a broad range of elements up to the iron group. Though rare nowadays,
they probably played a disproportionate role in shaping the evolution of the universe
following the formation of its first stars.
1 Introduction
Despite their scarcity, massive stars illuminate the universe disproportionately. They
light up regions of star formation and stir the media from which they are born. They
are the fountains of element creation that make life possible. The neutron stars and
black holes that they make are characterized by extreme physical conditions that can
never be attained on the earth. They are thus unique laboratories for nuclear physics,
magnetohydrodynamics, particle physics, and general relativity. And they are never
quite so fascinating as when they die.
Here we briefly review some of aspects of massive star death. The outcomes can
be crudely associated with three parameters - the star’s mass, metallicity, and rotation rate. In the simplest case of no rotation and no mass loss, one can delineate
five outcomes and assign approximate mass ranges (in some cases very approximate
mass ranges) for each. These masses then become the section heads for the first part
of this chapter. 1) From 8 to 30 M⊙ on the main sequence (presupernova helium
core masses up to 12 M⊙ ), stars mostly produce iron cores that collapse to neutron
stars leading to explosions that make most of today’s observable supernovae and
Stan Woosley
Department of Astronomy and Astrophysics, UCSC, Santa Cruz CA 95064 USA
e-mail: [email protected]
Alexander Heger
School of Mathematical Sciences, Monash University, Victoria 3800, Australia
e-mail: [email protected]
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S. E. Woosley and Alexander Heger
heavy elements. Within this range there are probably islands of stars that either do
not explode or explode incompletely and make black holes, especially for helium
cores from 7 to 10 M⊙ . 2) From 30 to 80 M⊙ (helium core mass 10 to 35 M⊙ ),
black hole formation is quite likely. Except for their winds, stars in this mass range
may be nucleosynthetically barren. Again though there will be exceptions, especially when the effects of rotation during core collapse are included. 3) 80 to (very
approximately) 150 M⊙ (helium cores 35 to 63 M⊙ ), pulsational-pair instability supernovae. Violent nuclear-powered pulsations eject the star’s envelope and, in some
cases, part of the helium core, but no heavy elements are ejected and a massive black
hole of about 40 M⊙ is left behind. 4) 150 - 260 M⊙ (again very approximate for the
main sequence mass range, but helium core 63 to 133 M⊙ ), pair instability supernovae of increasing violence and heavy element synthesis. No gravitationally bound
remnant is left behind. 5) Over 260 M⊙ (133 M⊙ of helium), with few exceptions,
a black hole consumes the whole star. Rotation generally shifts the main sequence
mass ranges (but not the helium core masses) downwards for each outcome. Mass
loss complicates the relation between initial main sequence mass and final helium
core mass.
The latter part of the paper deals with some possible effects of rapid rotation on
the outcome. In the most extreme cases, gamma-ray bursts are produced, but even
milder rotation can have a major affect on the light curve and hydrodynamics if a
magnetar is formed.
2 The Deaths of Stars 8 M⊙ to 80 M⊙
2.1 Compactness as a Guide to Outcome
The physical basis for distinguishing stars that become supernovae rather than planetary nebulae, and that are therefore, in some sense, “massive”, is the degeneracy
of the carbon-oxygen (CO) core following helium core burning. Stars with dense,
degenerate CO cores develop thin helium shells and eject their envelopes leaving
behind stable white dwarfs, while heavier stars go on to burn carbon and heavier
fuels. A mass around 8 M⊙ is usually adopted for the transition point. The effects of
degeneracy linger, however, on up to at least 30 M⊙ at oxygen ignition, and to still
heavier masses for silicon burning. Even at 80 M⊙ , the center of a massive star has
become degenerate by silicon depletion.
Were the core fully degenerate and composed of nuclei with equal numbers of
neutrons and protons, its maximum mass would be the cold Chandrasekhar mass,
1.38 M⊙ . This cold Chandrasekhar mass is altered however, both by electron capture reactions, which tend to reduce it, and the high temperatures necessary to burn
oxygen and silicon, which increase it (Chandrasekhar, 1939; Hoyle & Fowler, 1960;
Timmes, Woosley, & Weaver, 1996). For main sequence stars from 8 to 80 M⊙ , the
iron core mass at the time it collapses varies from about 1.3 to 2.3 M⊙ (baryonic
The Deaths of Very Massive Stars
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mass), with the larger values appropriate for more massive stars. Surrounding this
degenerate core is a nested structure of shells that cause adjustments to the density
structure. For very degenerate cores with energetic shells at their edges, the presupernova structure resembles that of an asymptotic giant branch star - a compact core
surrounded by thin burning shells and a low density envelope with little gravitational
binding energy. The matter outside of the iron core is easily ejected in such stars, and
it is easy to make a supernova out of them, even with an inefficient energy source
like neutrinos. Heavier stars with less degenerate cores and shells farther out, on the
other hand, have a density that declines more slowly. These mantles of heavy elements, where ultimately most of the nucleosynthesis occurs, are more tightly bound
and the star is more difficult to blow up.
O’Connor & Ott (2011) have defined a “compactness parameter”, ξ2.5 = 2.5/R2.5 ,
that is a quantitative measure of this density fall off. Here R2.5 is the radius, in
units of 1000 km, of the mass shell in the presupernova star that encloses 2.5 M⊙ .
The fiducial mass is taken to be well outside the iron core but deep enough in to
sample the density structure around that core. It makes little difference whether
this compactness is evaluated at the onset of hydrodynamical instability or at core
bounce (Sukhbold & Woosley, 2014). Figure 1 shows ξ2.5 as a function of main
sequence mass for stars of solar metallicity. O’Connor and Ott and Ugliano et al
(2012) have both shown that it becomes difficult to explode the star by neutrino
transport alone if ξ2.5 becomes very large. The critical value is not certain and may
vary with other properties of the star, but in Ugliano’s study is usually 0.20 to 0.30.
By this criterion, it may be difficult to explode stars in the 22 to 24 M⊙ range
(at least) as well as all stars above about 30 M⊙ that do not lose substantial mass
along the way to their deaths. The latter especially includes stars with very subsolar
metallicity.
There are a number of caveats that go along with this speculation. The structure
of a presupernova star is not fully represented by a single number and its compactness is sensitive to a lot of stellar physics, including the treatment of semiconvection and convective overshoot mixing and mass loss and the nuclear reaction rates
employed (Sukhbold & Woosley, 2014). Rotation and magnetic fields will change
both the presupernova structure and its prospects for explosion by non-neutrino processes. Finally, the surveys of how neutrino-powered explosions depend on compactness have, so far, been overly simple and mostly in 1D, though see recent work
by Janka and colleagues (Janka et al, 2012; Janka, 2012; Müller, Jamka, & Heger,
2012). Still the simplification introduced by this parametrization is impressive and
reasonably consistent with what we know about the systematics of supernova progenitors.
Figure 1 suggests that stars below 22 M⊙ should be, for the most part, easy
to explode using neutrinos alone and no rotation. This is consistent with the observational limits that Smartt (2009) and Smartt et al (2009) placed upon about a
dozen presupernova progenitor masses as well as the estimated mass of SN 1987A.
It also is a minimal set of masses if the solar abundances are to be produced
(Brown & Woosley, 2013). The compactness of stars between 22 and about 35 M⊙
is highly variable though due to the migration outwards of the carbon and oxy-
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S. E. Woosley and Alexander Heger
Fig. 1 Compactness parameter for presupernova stars of solar metallicity as a function of main
sequence mass (Sukhbold & Woosley, 2014). Stars with smaller ζ2.3 explode more easily.
gen burning shells (Sukhbold & Woosley, 2014). For a standard choice of stellar
physics, there exists an island of compact cores between 26 and 30 M⊙ that might
allow for islands of “explodability”. This would help with nucleosynthesis and also
possibly have implications for the properties of the Cas A supernova remnant. Cas
A, like SN 1993J and 2001gd (Chevalier & Soderberg, 2010), is thought to be the
remnant of a relatively massive single star that lost most of its hydrogenic envelope
either to a wind or a binary companion, yet its remnant contains a neutron star. If the
mass loss was to a companion, as is currently thought, then the progenitor mass was
probably less than 20 M⊙ , but if a star of 30 M⊙ could explode after losing most of
its envelope, this might provide an alternate, solitary star explanation.
On the other hand, binary x-ray sources exist and the black holes in them are
thought to be quite massive (Özel et al, 2010; Wiktorowicz, Belczynski, & Maccarone,
2014). Stars above 35 M⊙ either make black holes if their mass loss during the WolfRayet stage is small, or some variant of Type Ibc supernovae if it is large and shrinks
the carbon oxygen core below about 6 M⊙ .
Probably the greatest omission here is the effect of rotation and the need to produce gamma-ray bursts in a subset of stars. We also have said nothing about the fate
of stars over 80 M⊙ . Both topics will be covered in later sections.
The Deaths of Very Massive Stars
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2.2 8 M⊙ to 30 M⊙ ; Today’s Supernovae and Element Factories
For reasonable choices of initial mass function, stars in this mass range are responsible for most of the supernovae we see today and for the synthesis of most of the
heavy elements. This does not preclude many of these stars from making black
holes, but the supernovae we see are in this range. Baring binary interaction, including mergers, or low metallicity, such stars are, at death, red supergiants, and so
the most common supernovae are Type IIp. Explosion energies range from 0.5 to
4 × 1051 erg with a typical value of 9 × 1050 erg (Kasen & Woosley, 2009). These
values are the kinetic energy of all ejecta at infinity and the actual energy requirement for the central engine may be larger, especially for more massive stars with
large binding energies in their mantles. The light curves and spectra of the models
are consistent with observations, to the extent that models for SN IIp can even be
used as “standard candles” based upon the expanding photosphere method.
Including binary interactions, one can account for the remainder of common
(non-thermonuclear) supernovae, including Type Ib, Ic, IIb, etc (Dessart et al, 2011,
2012). These events typically come from massive stars in the 12 - 18 M⊙ range that
lose their binary envelopes and die as stripped down helium cores of 3 to 4 M⊙ . On
the low end, the explosion ejects too little 56 Ni to be a bright optical event. Heavier
stars are rarer and may not explode. If they do their light curves are broader and
fainter than typical Ib and Ic supernovae.
The nucleosynthesis produced by solar metallicity stars in this mass range has
been explored many times (Woosley & Weaver, 1995; Woosley, Heger, & Weaver,
2002; Woosley & Heger, 2007; Thielemann, Nomoto, & Hashimoto, 1996; Nomoto et al,
2006; Limongi, Straniero, & Chieffi, 2000; Chieffi & Limongi, 2004, 2013; Hirschi, Meynet, & Maeder,
2005; Nomoto, Kobayshi, & Tominaga, 2013). While the results from the different
groups studying the problem vary depending upon the treatment of critical reaction
rates, mass loss, semiconvection, convective overshoot, and rotationally induced
mixing, some general conclusions may be noted.
• The majority of the elements and their isotopes from carbon (Z = 6) through
strontium (Z = 38) are made in solar proportions in supernovae with an average
production factor of around 15 (IMF averaged yield expressed as a mass fraction
and divided by the corresponding solar mass fraction). The iron group, Ti through
Ni, is underproduced in massive stars by a factor of several, which is consistent
with the premise that most of the solar abundances of these species were made
recently in thermonuclear (Type Ia) supernovae. In the distant past, the oxygen
to iron ratio was larger, and massive stars probably produced the iron group in
very low metallicity stars.
• For a reasonable choice for the critical 22 Ne(α ,n)25Mg reaction rate, the light sprocess up to A = 90 is made well in massive stars, but only if the upper bound for
the masses of stars that explode is not too low (Brown & Woosley, 2013). The
heavy component of the p-process above A = 130 is also produced in massive
stars, but the production of the lighter p-process isotopes (A = 90 - 130) remains
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a mystery, especially the origin of the abundant closed shell nucleus 92 Mo (Z =
42, N = 50).
• While oxygen is definitely a massive star product, the elemental yield of carbon
(12 C) is sensitive to how mass loss is treated and requires for its production the
inclusion of the winds of stars heavier than 30 M⊙ . Red giant winds, AGB mass
loss, and planetary nebulae also produce 12 C, perhaps most of it, as well as all of
13 C and 14 N. 15 N and 17 O are not sufficiently produced in massive stars and may
be made in classical novae.
• 11 B and about one-third of 19 F are made by neutrino spallation in massive star
supernovae. 6 Li, 9 Be, and 10 B do not appear to be substantially made, and probably owe their origin to cosmic ray spallation in the interstellar medium. Some
but not all of 7Li is made by neutrino spallation.
• Certain select nuclei like 44 Ca, 48 Ca, and 64 Zn are underproduced and may require alternate synthesis
In addition to the previously mentioned uncertainties affecting presupernova evolution, assumptions about the explosion mechanism also play a major role. Fundamentally important is just which masses of stars eject their mantles of heavy elements and which collapse to black holes while ejecting little new elements. For a
given presupernova structure, a shock that imparts ∼1051 erg of kinetic energy to
the base of the ejecta, none of which fall back, will give a robust pattern of nucleosynthesis whether that energy is imparted by a piston or as a thermal “bomb”.
The approximation used by many, however, that the explosion across all masses
can be parametrized by a constant kinetic energy at infinity is too crude and needs
revisiting. Stars of different masses have different binding energies, compactness
parameters, and iron core masses. Rotation probably has a major effect on the explosion, especially of the more massive stars. The next stage of modeling will need
to take into account these dependencies.
2.3 Stars 30 M⊙ to 80 M⊙; Black Hole Progenitors
While the jury is still out regarding the mass-dependent efficiency of an explosion
mechanism that includes realistic neutrino transport, rotation, magnetic fields, and
relativity in three dimensions, the existence of stellar mass black holes and the absence of observable supernova progenitors with high mass implies that at least some
stars do not explode and eject all of their heavy element inventory. Until such time as
credible models exist, a reasonable assumption is that the success of the explosion is
correlated with the compactness (O’Connor & Ott, 2011; Ugliano et al, 2012). By
this criterion, one expects the central regions of stars with helium cores much larger
than about 10 M⊙ and lighter than 35 M⊙ to collapse (Sukhbold & Woosley, 2014)
to black holes. Above 10 M⊙ of helium, or about 30 M⊙ on the main sequence,
the iron core is large, typically over 2.0 M⊙ and the compactness parameter is large.
Above 35 M⊙ , or about 80 M⊙ on the main sequence, one encounters the pulsational
pair instability (Section 3).
The Deaths of Very Massive Stars
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For solar metallicity stars, mass loss may reduce the presupernova mass of the
star to a level where it can frequently explode. If it does and the entire envelope has
been lost, the explosion will be some sort of Type Ib or IC supernova. Because of
the large mass, the light curve would be broad, and not as bright as most observed
SN Ibc. The remnant would probably be a neutron star. It is unclear if such events
have been observed, though Cas A might be a candidate.
Even if the core of the star collapses to a black hole, its death is not necessarily nucleosynthetically barren or unobservable. The black hole could result from
fall back and the envelope may still be ejected. Even if the presupernova star does
not explode at all, its evolution will still have contributed to nucleosynthesis by its
wind, which may be appreciable (Hirschi, Meynet, & Maeder, 2005). If only the
hydrogenic layers are ejected, these winds can be a rich source of 12 C, 16 O and, at
low metallicity, 14 N (Meynet, 2002). If the wind eats deeply into the helium core,
18 O and 22 Ne can also be ejected, but the winds of such stars are devoid of heavier
elements like silicon and iron.
If the star rotates sufficiently rapidly, a gamma-ray burst may result (Section
6.2) or a magnetar-powered supernova. Even for non-rotating stars, it is debatable
whether the star can simply disappear without a trace. The sudden loss of mass
energy from the protoneutron star can trigger mass ejection and a very subluminous
supernova (Lovegrove & Woosley, 2013). Pulsations or gravity waves generated in
the final stages of evolution may partly eject the envelope. Even a weak explosion
might produce a potentially observable bright spike as its shock wave erupts through
the surface of the star (Piro, 2013). In a tidally locked binary or a low metallicity blue
supergiant with diminished mass loss, sufficient angular momentum may exist in the
outermost layers of the star to pile up in an accretion disk around the new black hole
producing some sort of x-ray and gamma-ray transient (Woosley & Heger, 2012;
Quataert & Kasen, 2012).
2.4 Yesterday’s Metal Poor Stars
Stars with lower metallicity, as may have predominated in the early universe, can
have different presupernova structures for a variety of reasons (Sukhbold & Woosley,
2014). Most importantly, metallicity affects mass loss, especially for the more massive stars. If the amount of mass lost is low or zero, the presupernova star including
its helium core, is larger, and that has a dramatic effect on its compactness and explodability. A vastly different outcome is expected for e.g., a 60 M⊙ star that retains
most of its hydrogen envelope and dies with a helium core of 24 M⊙ , and one that
loses all of its envelope as well as most of its helium core to die with a total mass
of 7.3 M⊙ . This small mass is obtained with current estimates of mass loss for solar
metallicity stars (Woosley, Heger, & Weaver, 2002). Indirect effects can also come
into play. Because a low metallicity star loses less mass, it loses less angular momentum and thus dies rotating more rapidly. Indeed, there is some suggestion from
theory that massive stars are all born rotating near break up and only slow as a conse-
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S. E. Woosley and Alexander Heger
quence of evolution (expansion) and mass loss (Rosen, Krumholz, & Ramirez-Ruiz,
2012).
Very low metallicity may also enhance the probability of forming more massive
stars (Abel et al, 2002). Whether this results in much more massive stars than are
being born today is being debated. While this is an important issue for the frequency
of first generation stars with masses over 80 M⊙ (Section 3), an equally important
question is whether the IMF for the first generation stars might have been “bottomlight”, that is producing a deficiency of stars below some characteristic mass, say
∼30 M⊙ (Tan & McKee, 2004). Since this would remove the range of masses responsible for most supernovae and nucleosynthesis today, the early universe would
have been quite a different place.
Even assuming the exact same masses of stars and explosions as today, nucleosynthesis would be distinctly different in low metallicity stars. The amount of neutrons available to produce all isotopes except those with Z = N depends on the
“neutron excess”, η = Σ (Ni − Zi )(Xi /Ai ), where Zi , Ni , and Ai are the proton number, neutron number and atomic weight of the species “i” and XI is its mass fraction.
At the end of hydrogen burning all CNO (essentially the metallicity of the star) has
become 14 N. Early in helium burning this becomes 18 O by the reaction sequence
14
N(α , γ )18 F(e+ ν )18 O. The weak interaction here is critical as it creates a net neutron excess that persists throughout the rest of the star’s life and limits the production
of neutron rich isotopes (like 22 Ne, 26 Mg, 30 Si etc) and odd-Z elements (like Na, Al,
P). Other weak interactions in later stages of evolution also increase η , so that by
the time one reaches calcium, the dependence on initial metallicity is not so great,
but one does expect an affect on the isotopes from oxygen through phosphorus.
Assuming that the IMF was unchanged and using the same explosion model as
for solar metallicity stars (but suppressing mass loss) gives an abundance set that
agrees quite well with observations of metal-deficient stars in the range -4 < [Z/Z⊙ ]
< -2 (Lai et al, 2008). All elements from C through Zn are well fit without the need
for a non-standard IMF or unusually high explosion energy.
Below [Z/Z⊙ ] = -4, one becomes increasing sensitive to individual stellar events
and to the properties of the first generation stars. If the stars below 30 M⊙ are removed from the sample, the nucleosynthesis is set by a) the pre-collapse winds of
stars in the 30 - 80 M⊙ range; b) the results of rotationally powered explosions
with uncertain characteristics; and c) the contribution of pulsational pair- and pairinstability supernovae (see below). If only a) and c) contribute appreciably, the resulting nucleosynthesis could be CNO rich and very iron poor.
The light curves of metal deficient supernovae below 80 M⊙ are likely to be
different - some of the time. If the stars die as red supergiants, then very similar
Type IIp supernovae will result, but more of the stars are expected to die as blue supergiants with light curves like SN 1987A (Heger & Woosley, 2010). Rotation can
alter this conclusion, however, as it tends to increase the number of red supergiants
compared with blue (Maeder & Meynet, 2012). To the extent that the massive stars
retain their hydrogenic envelope, Type Ib and Ic supernovae will be suppressed,
though of course a binary channel remains a possibility.
The Deaths of Very Massive Stars
9
3 Pulsational Pair Instability Supernovae (80 to 150 M⊙ )
The pair instability occurs during the advanced stages of massive stellar evolution
when sufficiently high temperature and low density lead to a thermal concentration
of electron-positron pairs sufficient to have a significant effect on the equation of
state. Only the most massive stars have sufficiently high entropy to encounter this
instability. Making the rest mass of the pairs in a post-carbon burning star takes energy that might have otherwise contributed to the pressure. As a result, for a time, the
pressure does not rise rapidly enough in a contracting stellar core to keep pace with
gravity. The structural adiabatic index of the core dips below 4/3 and, depending on
the strength of the instability, the core contracts more or less rapidly to higher temperature, developing considerable momentum as it does so. As temperature rises,
carbon, oxygen and, in some cases, silicon burn rapidly. The extra energy from this
burning, plus the eventual partial recovery from the instability when the pairs become highly relativistic, causes the pressure to rebound fast enough to slow the collapse. If enough burning occurs before the infall momentum becomes too great, the
collapse is reversed and an explosion is possible. For stars that are too big though,
specifically for helium non-rotating cores above 133 M⊙ , the collapse continues to
a black hole.
When an explosion happens, it can be of two varieties. If enough burning occurs
to unbind the star in a single pulse, a “pair-instability supernova” results (Section 4).
If not, the core of the star expands violently for a time and may kick off its outer
layers, including any residual hydrogen envelope. It then slowly contracts until the
instability is encountered again and the core pulses once more. The process continues until enough mass has been ejected and entropy lost as neutrinos that the pair
instability is finally avoided and the remaining star evolves smoothly to iron core
collapse. Typically this requires a reduction of the helium and heavy element core
mass to below 40 M⊙ . These repeated thermonuclear outbursts can have energies
ranging from “mild”, barely able to eject even the loosely bound hydrogen envelope
of a red supergiant, to extremely large, with over 1051 erg in a single pulse. On the
high energy end, collisions of ejected shells can produce very bright transients. The
observational counterpart is “pulsational pair-instability supernovae” (PPSN).
Depending upon rotation, the electron-positron pair instability begins to have a
marked effect on the post-carbon burning evolution of massive stars with negligible
mass loss when their main sequence mass exceeds about 70 - 80 M⊙ . (Extremely
efficient rotationally-induced mixing leading to chemically homogeneous chemical
evolution can reduce the threshold main sequence mass still further to approximately
the threshold helium core mass (Chatzopoulos & Wheeler, 2012)). For solar metallicity, stars this massive are usually assumed to lose all their hydrogen envelope and
part of their cores along the way and thus avoid the instability. Suffice it to say that
if the combined effects of mass loss and rotation allow the existence of a helium
core mass in excess of 34 M⊙ at carbon depletion, the pair instability will have an
effect. To get a full-up pair instability supernova, one needs a helium core mass of
about 63 M⊙ which might correspond, depending upon the treatment of convection
physics, to a main sequence star around 150 M⊙ . In between, lies the PPSN. As we
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S. E. Woosley and Alexander Heger
shall see, the final evolution of such stars can be quite complicated because of the
many pulses, but they have the merit that the explosion hydrodynamics is simple.
3.1 Pulsationally Unstable Helium Stars
While the observable display is quite sensitive to whether the presupernova star
retains its hydrogen envelope or not, the number, energies, and duration of the pulses
driven by the pair instability is determined entirely by the helium core mass. One can
thus sample the broad properties of PPSN using only a grid of bare helium cores.
This has the appealing simplicity of removing the uncertain effects of convective
dredge up and rotational mixing during hydrogen burning and reducing the problem
to a one parameter family of outcomes. Table 1 and Figure 2 summarize some recent
results for helium cores of various masses.
Initially, the instability is quite mild and only happens very close to the end of
the star’s life, after it has already completed core oxygen burning and is burning
oxygen in a shell. For larger helium core masses, a few pulses contribute sufficient
energy (about 1048 erg), that starting at around 34 M⊙ , the hydrogen envelope is
ejected, but little else. The low energy ejection of the envelope produces very faint,
long lasting Type IIp supernovae. The continued evolution of such stars yields an
iron core of about 2.5 M⊙ that almost certainly collapses to a black hole with a
mass nearly equal to the helium core mass. Thus the ejection of the envelope and its
nucleosynthesis are the only observables for a distant event.
Table 1 Pulses from Helium Core Explosions of Different Masses (M⊙ )
Mass
N Pulse
Duration
Energy
Rem. Mass
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
weak
12
many
many
many
18
10
10
7
4
4
2
2
2
2
2
1
1
4.0(3)
6.5(3)
1.4(4)
8.7(4)
2.8(5)
3.3(5)
9.0(5)
2.2(6)
6.4(6)
7.1(7)
4.3(8)
5.4(10)
1.3(11)
3.0(11)
1.3(11)
5.3(11)
-
1.6(45)
1.5(48)
9.2(48)
1.1(50)
2.7(50)
2.4(50)
5.8(50)
6.6(50)
9.2(50)
8.1(50)
8.1(50)
1.6(51)
1.6(51)
3.7(51)
2.7(51)
7.1(51)
4.7(51)
6.8(51)
32
33.93
35.81
37.29
38.24
39.72
39.94
41.27
41.52
42.80
45.87
43.35
40.61
17.06
36.60
5.33
0
0
The Deaths of Very Massive Stars
11
Moving on up in mass, the pulses have more energy, start earlier, and increase
in number until, above 42 M⊙ , their number starts to decline again. Figure 2 shows
that in the mass range 36 M⊙ to about 44 M⊙ a major pulse is typically preceded by
a string of smaller ones that grow in amplitude until a single violent event causes
a major change in the stellar structure. Recovery from this violent event requires a
Kelvin-Helmholtz time scale (τKH ∼ GM 2 /RL) for the core to contract back to the
unstable temperature, around 2 × 109 K. If the pulse is a weak one, the luminosity in
the Kelvin-Helmholtz time scale is the neutrino luminosity and is large, making the
time scale short. If the pulse decreases the central temperature below a half-billion
degrees however, radiation transport enters in and the time scale becomes long. On
the heavier end of this mass range, the total energy of pulses is a few times 1050
erg, but their overall duration is less than a week. Since this is less than the time
required for the ejected matter to become optically thin, the collisions are usually
finished before any supernova becomes visible. Depending upon the presence of an
envelope, one expects, for these cases, a rather typical Type Ib or IIp light curve,
with some structure possible in the case of the bare helium core because of its short
shock transversal time (Section-3.2). When the pulses are over, a large iron core
is again produced, and, some time later, the remaining core of helium and heavy
elements probably becomes a black hole.
For still heavier helium core masses, 44 to 52 M⊙ , the total energy of the pulses
becomes that of a typical supernova, but spread over several pulses that require from
weeks to years to complete. An important alignment of time scales occurs in this
mass range. For the masses and energies ejected, average shell speeds for the first
pulse are a few thousand km s−1 (much less if a hydrogen envelope is in the way).
At this speed, a radius of ∼1016 cm is reached in about a year, which is comparable
to the interval between pulses. Repeated supernovae and supernovae with complex
light curves are thus possible. The photospheric radii of typical supernovae in nature are a few times 1015 cm, this being the distance where the expanding debris
most efficiently radiate away their trapped energy on an explosive time scale. Since
the ejecta of a given pulse will consist of material moving both slower than and
faster than the average, and because each pulse is typically more energetic than its
predecessor, shells collide at radii 1015 − 1016 cm (Figure 3).
These collisions convert streaming kinetic energy to optical light with high efficiency. In principle, a substantial fraction of the total kinetic energy of the pulses
can be radiated, especially if the shells all run into a slowly moving hydrogen shell
ejected in the first pulse. Stars in this mass range, in the most extreme cases, can
thus give repeated supernovae with up to 1051 erg of light.
Still more energetic and less frequent pulsations happen at higher mass, but now
the presence of the envelope becomes critical. Without a hydrogen envelope, the
time between pulses is so long that the collisions happen at very large radii, 1017
- 1018 cm. For these very large radii, the result would not be so different from an
ordinary 1051 erg supernova running into an unusually dense interstellar medium.
Both the very large radii and long time scales preclude any resemblance to ordinary
optical supernovae, but the events might instead present as bright radio and x-ray
transients.
12
S. E. Woosley and Alexander Heger
Fig. 2 Pair-driven pulsations cause rapid variations in the central temperature (109 K) near the
time of death for helium cores of 32, 36, 40, 44, 48, 52 (on two different time scales) and 56 M⊙
(left to right; top to bottom). The log base 10 of the time scales (s) in each panel are respectively
4, 4, 5, 5, 6, 8, 7, and 10. The last rise to high temperature marks the collapse of the iron core to a
compact object. More massive cores have fewer, less frequent, but more energetic pulses. All plots
begin at central carbon depletion.
The Deaths of Very Massive Stars
13
Fig. 3 Velocities (solid lines) and radii (dashed lines) of ejected shells for four helium cores producing mass ejection by the pulsational pair mechanism. The velocities are evaluated at various
times when the collision between shells is underway. For the 42 and 48 M⊙ models. this was near
iron core collapse. For 52 M⊙ , it was at central silicon depletion, and for 56 M⊙ , after a strong
silicon flash, but before the re-ignition of silicon. Some merging of pulses has already occurred.
Regions of flat velocity imply spatially thin, high density shells that may be unstable in two or
three dimensions.
In the presence of an envelope, the first pulse does not eject matter with such high
speed and, given the large variation in speed from the inner part of the moving shell
to its outer extremity, substantial energy could still be emitted by explosions in this
mass range by shells colliding inside of 1016 cm making a bright Type II supernova.
Pulses continue until the helium core has lost enough mass to be stable again.
This gives a range of remnant masses typically around 34 to 46 M⊙ (Table 1). The
iron core masses and compactness parameters for these stars are both very large, so
it seems very likely that black holes will result for the entire range of stars making
PPSN, all having typical masses around 40 M⊙ .
14
S. E. Woosley and Alexander Heger
3.2 Light Curves for Helium Stars
Light curves for a sample of helium core explosions are shown in Figure 4 and illustrate the characteristics discussed in the previous section. For the lighter helium
cores, the pulses only eject a small amount of matter with low energy. Shell collisions are over before light escapes from the collision region. The light curve for
the 26 M⊙ helium core is typical for this mass range - a subluminous “supernova”
of less than 1042 erg s−1 lasting only a few days. These might be looked for in the
case of stars that have lost their envelopes prior to exploding. In a star with an envelope, as we shall see later, the situation would be very different. Even the small
(1049 erg) kinetic energy would unbind the envelope producing a long, faint Type
IIp supernova.
For the 42M⊙ helium core, a brighter, longer lasting transient is produced, but
still only a single event, albeit a structured one. The total duration of pulses is about 2
days, followed by a 2 day wait until the core collapse. The last pulse is a particularly
violent one. The light curve (Figure 4) shows a faint outburst occurring as many
smaller pulses merge and the first big of mass is ejected, followed by a longer more
luminous peak as that main pulse runs into the prior ejecta. Both of these transients
are quite blue since the collisions are occurring at small radius, a few times 1014 cm.
By 48 M⊙ , the shell collisions are becoming sufficiently energetic and infrequent
that the light curve fractures into multiple events. The collisions are now happening
at around 1015 cm and should be quite bright optically. At 52 M⊙ , one sees repeated
individual supernovae. Figure 4 merely shows the brightest one from this object.
Activity at the 1041 erg level started two years before.
It should be noted, though, that all these 1D light-curve calculations are quite approximate and need to be repeated in a multi-dimensional code with the appropriate
physics, especially for cases where the shells collide in an optically thin regime. KEPLER, a one dimensional implicit hydrodynamics code with flux-limited radiative
diffusion does an admirable job in a difficult situation. In 1D however, the snowplowing of a fast-moving shell into a slower one generates a large spike in density,
with variations of many orders of magnitude in density between one zone and an
adjacent one. For a time this thin shell corresponds to the photosphere. The “linearized” equations of hydrodynamics do not behave well in such clearly non-linear
circumstances and the outcome of a multi-dimensional calculation may be qualitatively different. This is an area of active research.
3.3 Type II Pulsational Pair Instability Supernovae
The retention of even a small part of the original hydrogen envelope significantly
alters the dynamics and appearance of PPSN. For example, what wold have been a
brief, faint transient for a 36 M⊙ helium core (Figure 4), provides more than enough
energy to eject the entire envelope of a red supergiant. A great diversity of outcomes
The Deaths of Very Massive Stars
15
Fig. 4 Bolometric light curves from pulsational pair instability supernovae derived from bare helium cores of 36, 42, 48 and 50 M⊙ . A wide variety of outcomes is possible. For the 36 and 42 M⊙
models the photospheric radius is inside 1015 cm and the transients will be blue. For the higher two
masses, the photosphere is near 1015 cm and the transients might have colors more like an ordinary
supernova.
is possible depending upon the mass of the envelope and helium core and the radius
of the envelope
Most striking are the “ultra-luminous supernovae” of Type IIn that happen when
very energetic pulses from the edge of the helium core strike a slowly moving, previously ejected hydrogen envelope. A similar (Type I) phenomenon could happen
for bare helium cores, but probably with a shorter-lived, less luminous light curve
owing to the smaller masses involved. An example is shown in Figure 6 based upon
the evolution of a 110 M⊙ star (Woosley, Blinnikov, & Heger, 2007). By the end
of its life this star had shrunk to 74.6 M⊙ (using a wholly artificial mass loss rate),
of which 49.9 M⊙ was the helium core. This core experienced three violent pulsations. The first ejected almost all of the hydrogen envelope, leaving 50.7 M⊙ behind.
This envelope ejection produced a rather typical Type IIp supernova although with
a slower than typical speed and luminosity (Figure 5). By 6.8 years later, the stellar
remnant had contracted to the point that it experienced the pair instability again.
Two more pulses, occurring in rapid succession, ejected an additional 5.1 M⊙ with
16
S. E. Woosley and Alexander Heger
Fig. 5 Light curves of the two supernovae produced by the 110 M⊙ PPSN
(Woosley, Blinnikov, & Heger, 2007). The first pulse ejects the envelope and produces the
faint supernova shown in greater detail on the right. 6.8 years later the collision of pulses 2 and 3
with that envelope produces another brighter outburst (see Figure 6)
a total kinetic energy of 6 × 1050 erg. Pulses 2 and 3 quickly merged and then run
into the ejected envelope (Figures 5 and 6).
These light curves were calculated using 1D codes in which the collision of the
shells again produced a very large density spike. When the calculation was run again
in 2D, but without radiation transport (Figure 6), a Rayleigh-Taylor instability developed that led to mixing and a greatly reduced density contrast. The combined
calculation of multi-D hydro coupled to radiation transport has yet to be carried out,
so the light curves shown here are to be used with caution, but a multi-dimensional
study would probably give a smoother light curve.
3.4 Nucleosynthesis
The nucleosynthesis from PPSN is novel in that it is heavily weighted towards the
light species that are ejected in the shells. For present purposes, given the large iron
cores, we assume that all matter not ejected by the pulsations becomes a black hole.
This assumption could be violated if rapid rotation energized some sort of jet-like
outflows (e.g., a gamma-ray burst), but otherwise it seems reasonable.
Table 2 gives the approximate bulk nucleosynthesis, in solar masses, calculated
for our standard set of helium cores models. For the lightest cores, the pulses lack
sufficient energy to eject more than a small amount of surface material, which by
assumption here is pure helium. It should be noted, however, that even these weak
explosions would eject at least part of the hydrogen envelope of any red supergiant
(typical binding energy less than 1048 erg). Since these envelopes often produce
primary nitrogen by mixing between the helium core and hydrogen burning shell,
an uncertain but possibly large yield of carbon, nitrogen, and oxygen (and of course
The Deaths of Very Massive Stars
17
Fig. 6 Left: Light curve for the second very luminous outburst of the 110 M⊙ model (see Figure 5)
of the two supernovae produced by the 110 M⊙ PPSN (Woosley, Blinnikov, & Heger, 2007). The
brighter set of curves results hen the collision speed is artificially increased by a factor of 2 and resembles SN 2006gy. Right: 2D calculation of the explosion of a 110 M⊙ star as a PPSN. The dense
shell produced in 1D by the collision of the ejecta from two pulse is Rayleigh-Taylor unstable. The
resulting density contrast is much smaller.
hydrogen and helium) would accompany these explosions in a star that had not lost
its envelope.
Moving up in mass, the violence of the pulses increases rapidly and more material
is ejected, eventually reaching the deeper shells rich in heavier elements. In Table 2,
total yields of less than 0.01 M⊙ have not been included with the single exception
of the 66 M⊙ model which made 0.037 M⊙ of 56 Ni. The 64 and 66 M⊙ models
are actually full up pair instability supernovae and leave no remnants, so perhaps
including their yields here with the PPSN is a bit misleading.
If one folds these yields with an IMF to get an overall picture of the nucleosynthesis from a generation of PPSN, it is clear that the production (and the typical spectra
of PPSN) will be dominated by H, (He), C, N, O, (Ne) and Mg and little else. In
particular, PPSN make no iron-group elements. Given the dearth of strong He and
Ne lines, one might expect that the generation of stars following a putative “first
generation” of PPSN would show enhancements of C, N, O, and Mg and be “ultrairon poor”. Of course some heavier elements could be made by stars sufficiently
light (main sequence mass less than 20 M⊙ ?) to explode by the neutrino-transport
process, or sufficiently heavy to make iron in a pair-instability supernova (helium
core mass over 65 M⊙ ).
4 150 to 260 M⊙ ; Pair Instability Supernovae
The physics of pair instability supernovae (PISN) is sufficiently well understood
that they can be accurately modeled in 1D on a desktop computer. A major ques-
18
S. E. Woosley and Alexander Heger
Table 2 Nucleosynthesis in Ejected Shells (M⊙ ) from Helium Core Pulsational Explosions
Mass
Total
He
C
O
Ne
Mg
Si
S
Ar
Ca
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
0.071
0.19
0.71
1.76
2.28
4.06
4.73
6.48
7.20
6.13
10.64
15.38
40.93
23.39
56.67
64
66
0.071
0.19
0.32
0.50
0.60
0.85
1.02
1.34
1.58
1.55
1.65
1.74
1.85
1.89
1.95
1.92
1.79
0095
0.29
0.43
0.79
0.94
1.40
1.60
1.33
1.83
2.06
2.87
3.10
2.87
3.62
3.60
0.17
0.53
0.70
1.36
1.61
2.30
2.61
2.29
5.32
9.41
30.5
15.0
37.5
44.1
42.8
0.096
0.32
0.41
0.80
0.90
1.15
1.16
0.81
1.35
1.52
2.64
2.49
2.60
3.60
3.99
0.032
0.11
0.14
0.26
0.27
0.30
0.26
0.16
0.41
0.50
1.42
0.60
1.43
2.12
2.07
0.001
0.074
0.15
1.49
0.28
6.39
5.35
7.11
0.17
0.058
2.99
2.41
3.49
0.020
0.008
0.51
0.43
0.60
0.015
0.005
0.44
0.38
0.53
tion though is their frequency in the universe. PISN come from a range of masses
somewhat heavier than we expect for presupernova stars today. This is not to say
that stars of over 150 M⊙ are not being born. See e.g., the review by Crowther reported in Vink et al (2013) which gives 320 M⊙ as the current observational limit.
The issue is whether such large masses can be retained in a star whose luminosity
hovers near the Eddington limit (Vink et al, 2011). Still observers claim to have discovered at least one PISN event (Galyam et al, 2009). Because the critical quantity
governing whether a star becomes PISN is the helium core mass of the presupernova star (greater than 65 M⊙ ), they are favored by diminished mass loss, i.e., at
low metallicity, and may have been more abundant in the early universe.
A common misconception is that all PISN make a lot of 56 Ni and therefore are
always very bright. As Figure 7 shows, large 56 Ni production and very high kinetic
energies are limited to a fairly narrow range of exceptionally heavy and rare PISN.
Most events will either present as a particularly energetic Type IIp supernova or a
subluminous SN I. For an appreciable range of masses, less 56 Ni is produced than
in, e.g., a SN Ia (about 0.7 M⊙ ).
The nucleosynthesis of very low metallicity PISN is quite distinctive because
they lack the excess neutrons needed to make odd-Z elements during the explosion.
This is because the initial metallicity of the star, mostly CNO, is turned into 14 N
during hydrogen burning. During helium burning, 14 N captures an alpha particle
experiencing a weak decay to make 18 O which has two extra neutrons. Subsequent
burning stages rearrange these neutrons using them to make isotopes and elements
that require an excess of neutrons over protons, like almost all odd Z elements do.
During the collapse phase, the time is too short for additional weak interactions so
the ejected matter ends up deficient in things like Na, Al, P, Cl, K, Sc, V, and Mn.
The Deaths of Very Massive Stars
19
Fig. 7 Nucleosynthesis in pair-instability supernovae as a function of helium core mass. Also given
is the explosion energy in units of 1051 erg (broad grey line) which rises steadily with mass. The
dark solid line is 56 Ni synthesis which is not particularly large below 90 M⊙ (Heger & Woosley,
2002).
Very metal poor stars show no such anomalies and this suggests that the contribution
of PISN to very early nucleosynthesis was small.
5 Above 260 M⊙
Stars heavier than 260 M⊙ , or more specifically non-rotating helium cores greater
than 133 M⊙ , are expected to produce black holes, at least up to about 105 M⊙ . Starting around 105 M⊙ , hydrogenic stars encounter a post-Newtonian instability on the
main sequence and collapse (Fowler & Hoyle, 1964). If these stars have near solar
metallicity (above Z = 0.005) then titanic explosions of 1056 - 1057 erg, powered
by explosive hydrogen burning, can result for masses in the range 105 - 106 M⊙
(Fuller, Woosley, & Weaver, 1986). Lacking a large initial concentration of CNO,
stars in this mass range, collapse to black holes.
For lighter stars, ∼103 - 105 M⊙ , hydrogen burns stably, but helium burning
encounters the pair instability, and on the upper end, the post-Newtonian instability.
Again black hole formation seems the most likely outcome, though this mass range
has not been fully explored.
20
S. E. Woosley and Alexander Heger
6 The Effects of Rotation
Rotation alters stellar evolution in two major ways. During presupernova evolution
it leads to additional mixing processes that can stir up either regions of the star or
the whole star. Generally the helium cores of rotating stars are larger and, since the
nucleosynthesis and explosion physics of massive stars depends sensitively upon the
helium core mass, the outcome of a smaller mass main sequence star with rotation
can resemble that of a larger one without rotation. The mixing can also increase
the lifetime of the star and its luminosity and bring abundances to the surface that
might have otherwise remained hidden. In extreme cases, rotation can even lead to
the complete mixing of the star on the main sequence, thus avoiding the formation
of a supergiant and producing a very rapidly rotating presupernova star that might
serve as a gamma-ray burst progenitor (Section 6.2).
The other way rotation changes the evolution is by affecting how the star
explodes and the properties of the compact remnant it leaves behind. Calculations that use reasonable amounts of rotation and approximate the effects of magnetic torques in transporting angular momentum show that rotation may play an
increasingly dominant role in the explosion as the mass of the star increases
(Heger, Woosley, & Spruit, 2005). This is in marked contrast to the neutrino transport model which shows the opposite behavior (Section 2.1); heavier stars are more
difficult to explode with neutrinos.
Table 3 Pulsar Rotation Rate Predicted by Models (Heger, Woosley, & Spruit, 2005)
Mass
(M⊙ )
Baryon Gravitational
J
(M⊙ )
(M⊙ )
(1047
erg s)
BE
(1053
erg)
Pulsar P
(ms)
12
15
20
25
35
1.38
1.47
1.71
1.88
2.30
2.3
2.5
3.4
4.1
6.0
15
11
7.0
6.3
3.0
1.26
1.33
1.52
1.66
1.97
5.2
7.5
14
17
41
Table 3 shows the expected rotation rates of pulsars derived from the collapse of
rotating stars of various main sequence masses. The rotational energy of these neutron stars is given approximately by 1051 (5ms/P)−2 erg, where it is assumed that the
neutron star moment of inertia is 80 km2 M⊙ (Lattimer & Prakash, 2007). This implies that supernova over about 20 M⊙ or so have enough rotational energy to potentially power a standard supernova. Rapidly rotating stellar cores are also expected to
give birth to neutron stars with large magnetic fields (Duncan and Thompson, 1992),
thus providing a potential means of coupling the large rotation rate to the material
just outside the neutron star. Calculations so far are encouraging (e.g. Akiyama et al,
2003; Burrows et al, 2007; Janka, 2012). No calculation has yet modeled the full
history, of a rotational, or rotational plus neutrino powered supernova all the way
The Deaths of Very Massive Stars
21
through from the collapse to explosion phase including all the relevant neutrino and
MHD physics, but probably this will happen in the next decade.
In principle, the outcomes of rotationally powered supernovae and those powered by neutrinos should be very similar, though only rotation offers the prospect
of making the explosion hyper-energetic (much greater than 1051 erg). To the extent that nucleosynthesis, light curves and spectra only depend upon the prompt
deposition of ∼ 1015 erg at the center of a highly evolved red or blue supergiant,
they will be indistinguishable. Rotation breaks spherical symmetry and may produce jets, but except in the case of gamma-ray bursts, it may be hard to disentangle
effects essential to the explosion from those that simply modify an already successful explosion. There are interesting constraints on time scales, however, and hence
on field strengths. Rotation or neutrinos must overcome a ram pressure from accretion that, in the case of high compactness parameter, may approach a solar mass per
second. At a radius of 50 km, roughly typical of a young hot protoneutron star, it
would take a field strength of over 1015 gauss to impede the flow. A similar estimate
comes from nucleosynthesis. In order to synthesize 56 Ni, material must be heated
to at least 4 and preferably 5 × 109 K. In a hydrodynamical model in which radiation dominates and 1051 erg is deposited instantly, this will only occur in a region
smaller than 3000 km. It takes the shock, moving at typically 20,000 km s−1 , about
0.1 s to cross that region, after which it begins to cool off. To deposit 1051 erg in that
time with a standard dipole luminosity (Lang, 1980) the field strength would need
to exceed about 1016 gauss. This probably exceeds the surface fields generated by
collapse alone. Whether the magneto-rotational instability can generate such fields
is unclear, but it may take an exceptionally high rotation rate for this to all work out.
Perhaps the most common case is a neutrino-powered initial explosion amplified
by rotation at later times. If that is the case though, a successful outgoing shock must
precede any significant pulsar input. That starting point be difficult to achieve in
stars with high compactness (Figure 1). In any case we do know that some massive
stars do make black holes.
6.1 Magnetar Powered Supernova Light Curves
If magnetic fields and rotation can provide the ∼1051 erg necessary for the kinetic energy of a supernova, they might, with greater ease, deliver the 1048 or even
1050 erg needed to make a bright - or a really bright - light curve (Woosley, 2010;
Kasen & Bildsten, 2010). At the outset, one must acknowledge the huge uncertainty
in applying the very simple pulsar power formula (Lang, 1980),
dE
−4
≈ 1049 B215 Pms
erg s−1 ,
dt
(1)
to a situation where the neutron star is embedded in a dense medium and that is
still be rapidly evolving. Doing this blindly, however, yields some interesting results
(Figure 8). Since the energy is deposited late, it is less subject to adiabatic losses and
22
S. E. Woosley and Alexander Heger
is emitted as optical light with high efficiency. For reasonable choices of magnetic
field and initial rotation rate, the supernova can be “ultra-luminous”, brighter than a
typical SN Ia for a much longer time.
Fig. 8 Magnetar powered light curves for (left) different values of field strength (1014 , 1015 , and
1016 G at 4 ms) and (right) initial rotation periods (2, 4, 6 ms at 1014 G). The base event is the 1.2
×1051 erg explosion of a 10 M⊙ carbon-oxygen core. (Sukhbold and Woosley, 2014, in preparation)
The magnetic fields required are not all that large and are similar to what has been
observed for modern day magnetars (Mereghetti, 2008). In fact, too large a field results in the rotational energy being deposited too early. That energy then contributes
to the explosion kinetic energy, but little to the light curve because, by the time the
light is leaking out, the magnetar has already deposited most of its rotational energy. The rotation rates, though large, are also not extreme, not very different, in
fact, from the predictions for quite massive stars (Heger, Woosley, & Spruit, 2005).
If gamma-ray bursts are to be powered by millisecond magnetars with fields ∼1015
- 1016 G, and if ordinary pulsars have fields and rotational energies 100 to 1000
times less, one expects somewhere, sometime to make neutron stars with fields and
rotational energies that are just ten times less. The long tails on the light curves are
interesting and, lacking spectroscopic evidence or very long duration observations,
might easily be confused with 56 Co decay (Woosley, 2010).
Depending upon the mass and radius of the star, the presence or absence of a
hydrogenic envelope, and the supernova explosion energy, the resulting magnetarilluminated transients can be quite diverse. The brighter events will tend to be of
Type I because the supernova becomes transparent at an earlier time when greater
rotational energy is being dissipated. The upper bound to the luminosity is a few
times 1051 erg emitted over several months, or ∼1044.5 erg s−1 , but much fainter
events are clearly possible. For Type II supernovae in red supergiants, the magnetar contribution may present as a rapid rise in brightness after an extended plateau
(Maeda et al, 2007). The rise could be even more dramatic and earlier in a blue
supergiant.
The Deaths of Very Massive Stars
23
An interesting characteristic of 1D models for magnetar powered supernovae is
a large density spike caused by the pile up of matter accelerated from beneath by
radiation. In more than one dimension, this spike will be unstable and its disruption
will lead to additional mixing that might have consequences for both the spectrum
and the appearance of the supernova remnant.
6.2 Gamma-Ray Bursts (GRBs)
In the extreme case of very rapid rotation and the complete loss of its hydrogenic
envelope, the death of massive star can produce a common (long-soft) GRB. For
a recent review see Woosley (2013). There are two possibilities for the “central
engine” - a “millisecond magnetar” and a “collapsar”. The former requires that the
product of a successful supernova explosion be, at least for awhile, a neutron star,
and that the power source is its rotational energy. The latter assumes the formation
of a black hole with a centrifugally supported accretion disk. The energy source can
be either the rotational energy of that black hole or of the disk, which is, indirectly,
energized by the black hole’s strong gravity.
Both models require that the progenitor star have extremely high angular momentum in and around the iron core. Loss of the hydrogen envelope could occur
though a wind, binary mass exchange, or because extensive rotationally-induced
mixing on the main sequence kept a red giant from ever forming. Loss of the envelope by a wind is disfavored because the existence of a lengthy red giant phase
would probably break the rotation of the core to the extent that the necessary angular
momentum was lost. One is this left with the possibility of a massive star that lost its
envelope quite early in to a companion or a single star that experienced chemically
homogeneous evolution (Maeder, 1987; Woosley & Heger, 2006; Yoon & Langer,
2005, 2006). The resulting Wolf-Rayet star must also not lose much mass or its
rotation too will be prohibitively damped. This seems to exclude most stars of solar metallicity, so GRBs are relegated to a low metallicity population. The relevant
mass loss rate depends upon metallicity (specifically the iron abundance) as Z0.86
(Vink & de Koter, 2005), and even mild reduction is sufficient to provide the necessary conditions for a millisecond magnetar.
The collapsar model is capable, in principle, of providing much more energy (up
to ∼1054 erg) than the magnetar model (up to 3 × 1052 erg). The former is limited
only by the efficiency of converting accreted mass into energy, which can be quite
high for a rotating black hole, while the latter is capped by a critical rotation rate
where the protoneutron star deforms and efficiently emits gravitational radiation. So
far, there is no clear evidence for total (beaming corrected) energies above 1052.5 in
any GRB, so both models remain viable. It is interesting that there may be some pile
up of the most energetic GRBs and their associated supernovae around a few times
1052 . That might be taken as (mild) evidence in favor of the magnetar model. On the
other hand, black hole production is likely in the more massive stars and it may be
24
S. E. Woosley and Alexander Heger
difficult to arrange things such that all the matter always accretes without forming a
disk (Woosley & Heger, 2012)
Since angular momentum is in short supply, it is definitely easier to produce
a millisecond magnetar which requires a mass averaged of angular momentum of
only 2 × 1015 erg s (for a moment of inertia I = 1045 g cm2 ), or a value at its equator
of 6 × 1015 erg s (for a neutron star radius of 10 km). For comparison, the angular
BH
erg s and
momentum for the last stable orbit of a Kerr black hole is 1.5 × 1016 3MM
⊙
about three times larger for a Schwarzschild hole. The same sorts of systems that
make collapsars thus also seem likely to make, at least briefly, neutron stars with
millisecond rotation periods. How these rapid rotators make their fields and how
the fields interact with the rapidly accreting matter in which they are embedded is a
very difficult problem in 3D, general relativistic magnetohydrodynamics. Analytic
arguments suggest however that large fields will be created (Duncan and Thompson,
1992) and that the rotation and magnetic fields will play a major role in launching
an asymmetric explosion (Akiyama et al, 2003; Burrows et al, 2007).
Just which mass and metallicity stars make GRBs is an interesting issue. Even
when the effects of beaming are included, the GRB event rate is a very small fraction of the supernova rate and thus the need for special circumstances is a characteristic of all successful models. These special circumstances include, as mentioned, the lack of any hydrogenic envelope and very rapid rotation. Without magnetic torques, the cores of most massive stars would rotate so rapidly at death that
millisecond magnetars, collapsar, and presumably GRBs would abound. Any realistic model thus includes the effects of magnetic braking, even though the theory
(Spruit, 2002; Heger, Woosley, & Spruit, 2005) is highly uncertain. In fact, most
massive stars may be born with extremely rapid rotation, corresponding to 50%
critical in the equatorial plane, because of their magnetic coupling to an accretion
disk (Rosen, Krumholz, & Ramirez-Ruiz, 2012). The fact that most massive stars
are observed to be rotating more slowly on the main sequence is a consequence of
mass loss which would be reduced in regions with low metallicity. Since these large
rotation rates are sufficient, again with uncertain parameters representing the inhibiting effect of composition gradients, to provoke efficient Eddington-Sweet mixing on
the main sequence, GRBs should be abundant (too abundant?) at low metallicity. It
is noteworthy that models for GRBs that invoke such efficient mixing on the main
sequence do not require that the star be especially massive since, for low metallicity,
the zero age main sequence mass is not much greater than the presupernova helium
core mass (Woosley & Heger, 2006). A low metallicity star of only 15 M⊙ could
become a GRB and a star of 45 M⊙ could become a pulsational pair instability
supernova.
Using a standard set of assumptions, the set of massive stars that might make
GRBs by the collapsar mechanism has been surveyed for a grid of masses and metallicities by Yoon & Langer (2006). Averaged over all redshifts they find a GRB to
supernova event ratio of 1/200 which declines at low redshift to 1/1250. Half of all
GRBs are expected to be beyond redshift 4. Given that magnetars might also make
GRBs, or even most of them, these estimates need to be reexamined. In particular,
the mean redshift for bursts may be smaller and the theoretical event rate higher.
The Deaths of Very Massive Stars
25
7 Final Comments
As is frequently noted, we live in interesting times. Most of the basic ideas invoked
for explaining and interpreting massive star death are now over 40 years old. This
includes supernovae powered by neutrinos, pulsars, the pair-instability, and the pulsational pair instability. Yet lately, the theoretical models and observational data
have both experienced exponential growth, fueled on the one hand by the rapid expansion of computer power and the shear number of people running calculations,
and on the other, by large transient surveys. Ideas that once seemed “academic”,
like pair-instability supernovae and magnetar-powered supernovae are starting to
find counterparts in ultra-luminous supernovae.
“Predictions” in such a rapidly evolving landscape quickly become obsolete or
irrelevant. Still, it is worth stating a few areas of great uncertainty where rapid
progress might occur. These issues have been with us a long time, but problems
do eventually get solved.
• What range(s) of stellar masses and metallicities explode by neutrino transport
alone. The community has hovered on the brink of answering this for a long
time. Today some masses explode robustly and others show promise (Janka et al,
2012; Janka, 2012), but a comprehensive, parameter-free understanding is still
lacking. The computers, scientists, and physics may be up to the task in the next
five years. The compactness of the progenitor very likely plays a major role. It
would be really nice to know.
• What is the relation between the initial and final (presupernova) masses of stars
of all masses and metallicities. Suppose we knew the initial mass function at
all metallicities (a big given). What is the final mass function for presupernova
stars? We can’t really answer questions about the explosion mechanism of stars
of given main sequence masses without answering this one too. Our theories and
observations of mass loss are developing, but still have a long way to go.
• What is the angular momentum distribution in presupernova stars? To answer
this the effects of magnetic torques and mass loss must be included throughout
all stages of the evolution - a tough problem. Approximations exist, but they are
controversial and more 3D modeling might help.
• Are the ultra-luminous supernovae that are currently being discovered predominantly pair instability, pulsational pair instability, or magnetar powered (or all
three)? Better modeling might help, especially with spectroscopic diagnostics.
• Is the most common form of GRB powered by a rotating neutron star or by an
accreting black hole? What are the observational diagnostics of each?
• Does “missing physics”, e.g., neutrino flavor mixing or a radically different nuclear equation of state play a role in answering any of the above questions?
This small list of “big theory issues” of course connects to a greater set of
“smaller issues” - the treatment of semiconvection, convective overshoot, and rotational mixing in the models; critical uncertain nuclear reaction rates; opacities;
the complex interplay of neutrinos, magnetohydrodynamics, convection and general relativity in 3D in a real core collapse - well maybe that is not so small.
26
S. E. Woosley and Alexander Heger
Obviously there is plenty for the next generation of stellar astrophysicists to do.
Acknowledgements
We thank Tuguldur Sukhbold and Ken Chen for permission to include here details of
their unpublished work, especially Figures 1, 6, and 8. This work has been supported
by the National Science Foundation (AST 0909129), the NASA Theory Program
(NNX09AK36G), and the University of California Lab Fees Research Program (12LR-237070).
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